Efficient tensor decomposition over number systems beyond finite fields

Investigate whether efficient (polynomial-time) algorithms for low-rank tensor decomposition exist over number systems beyond finite fields, particularly over the integers, and develop corresponding algorithmic frameworks if feasible.

Background

Much practical interest lies in integer-only decompositions to avoid floating-point arithmetic. The paper focuses on finite fields and raises the question of extending efficient decomposition methods to other algebraic settings such as the integers.